Editing Statistical hypothesis test (section)

===Choice of null hypothesis===

[[Paul Meehl]] has argued that the [[epistemological]] importance of the choice of null hypothesis has gone largely unacknowledged. When the null hypothesis is predicted by theory, a more precise experiment will be a more severe test of the underlying theory. When the null hypothesis defaults to "no difference" or "no effect", a more precise experiment is a less severe test of the theory that motivated performing the experiment.<ref>{{cite journal|last=Meehl|first=P|year=1990|title=Appraising and Amending Theories: The Strategy of Lakatosian Defense and Two Principles That Warrant It|url=http://rhowell.ba.ttu.edu/meehl1.pdf|journal=Psychological Inquiry|volume=1|issue=2|pages=108–141|doi=10.1207/s15327965pli0102_1}}</ref> An examination of the origins of the latter practice may therefore be useful:

'''1778:''' [[Pierre Laplace]] compares the birthrates of boys and girls in multiple European cities. He states: "it is natural to conclude that these possibilities are very nearly in the same ratio". Thus, the null hypothesis in this case that the birthrates of boys and girls should be equal given "conventional wisdom".<ref name="Laplace 1778" />

'''1900:''' [[Karl Pearson]] develops the [[chi squared test]] to determine "whether a given form of frequency curve will effectively describe the samples drawn from a given population." Thus the null hypothesis is that a population is described by some distribution predicted by theory. He uses as an example the numbers of five and sixes in the [[Walter Frank Raphael Weldon|Weldon dice throw data]].<ref name="Pearson 1900">{{cite journal|last=Pearson|first=K|year=1900|title=On the criterion that a given system of deviations from the probable in the case of a correlated system of variables is such that it can be reasonably supposed to have arisen from random sampling|url=http://www.economics.soton.ac.uk/staff/aldrich/1900.pdf|journal=The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science|volume=5|issue=50|pages=157–175|doi=10.1080/14786440009463897}}</ref>

'''1904:''' [[Karl Pearson]] develops the concept of "[[contingency table|contingency]]" in order to determine whether outcomes are [[statistical independence|independent]] of a given categorical factor. Here the null hypothesis is by default that two things are unrelated (e.g. scar formation and death rates from smallpox).<ref name="Pearson 1904">{{cite journal|last=Pearson|first=K|year=1904|title=On the Theory of Contingency and Its Relation to Association and Normal Correlation|url=https://archive.org/details/cu31924003064833|journal=Drapers' Company Research Memoirs Biometric Series|volume=1|pages=1–35}}</ref> The null hypothesis in this case is no longer predicted by theory or conventional wisdom, but is instead the [[principle of indifference]] that led [[Ronald Fisher|Fisher]] and others to dismiss the use of "inverse probabilities".<ref>{{cite journal|last=Zabell|first=S|year=1989|title=R. A. Fisher on the History of Inverse Probability|journal=Statistical Science|volume=4|issue=3|pages=247–256|doi=10.1214/ss/1177012488|jstor=2245634|doi-access=free}}</ref>